They are called magic links... only thing magic about them is their ability to annoy me
And I think that subset is much larger than some would expect.
I sadly can't put my finger on what's so compelling about this, just that my "oh that person should talk to a UX team lead!" meter just went plink
It's only annoying if the site is constantly timing you out so that every single visit you need to resend. Why not just use secure cookies to remember the user for say a week?
I love them and prefer them to creating yet another account with a password.